Results 11 to 20 of about 60,649 (158)
Improper Graceful and Odd-graceful Labellings of Graph Theory [PDF]
arXiv, 2015 In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having ...
Wang, Hongyu, Xu, Jin, Yao, Bing
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On graceful difference labelings of disjoint unions of circuits [PDF]
Open Journal of Discrete Applied Mathematics, 2019 A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f between V and {1,...,|V|} such that, when each arc uv is assigned the difference label f(v)-f(u), the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases.
Christophe Picouleau, Alain Hertz
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Graceful Labellings of Various Cyclic Snakes [PDF]
arXiv, 2020 19 ...
Alkasasbeh, Ahmad H., Dyer, Danny
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On $k$-Super Graceful Labeling of Graphs [PDF]
arXiv, 2018 Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $p$ and size $q$. For $k\ge 1$, a bijection $f: V(G)\cup E(G) \to \{k, k+1, k+2, \ldots, k+p+q-1\}$ such that $f(uv)= |f(u) - f(v)|$ for every edge $uv\in E(G)$ is said to be a $k$-super graceful labeling of $G$.
Lau, Gee-Choon +2 more
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Graceful labeling of digraphs—a survey [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v) − g(u)) (mod q + 1) If the arc values are all distinct then the labeling is called a graceful labeling of digraph. In this survey article, we have
Shivarajkumar, M. A. Sriraj, S. M. Hegde
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Graceful labellings of variable windmills using Skolem sequences [PDF]
arXiv, 2021 In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings exist for windmills with $C_3$ and $C_4$ vanes, and infinite families of $3,5$-windmills and $3,6$-windmills.
Ahmad H. Alkasasbeh +2 more
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Graceful Labeling of Hypertrees
Journal of Mathematics Research, 2021 Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G (vertex labeling) or to edges of G (edge labeling) or both of them.
S. I. Abo El-Fotooh +3 more
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Graceful and Odd Graceful Labeling of Some Graphs [PDF]
International Journal of Mathematics and Soft Computing, 2013 In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.
Samir K. Vaidya, N. H. Shah
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On edge graceful labelings of disjoint unions of $2r$-regular edge graceful graphs [PDF]
arXiv, 2006 We prove that if $G$ is a $2r$-regular edge graceful $(p,q)$ graph with $(r,kp)=1$ then $kG$ is edge graceful for odd $k$. We also prove that for certain specific classes of $2r$-regular edge graceful graphs it is possible to drop the requirement that $(r,kp)=1$
Adrian Riskin, Georgia Weidman
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Radio Graceful Labelling of Graphs
Theory and Applications of Graphs, 2020 Radio labelling problem of graphs have their roots in communication problem known as \emph{Channel Assignment Problem}. For a simple connected graph $G=(V(G), E(G))$, a radio labeling is a mapping $f \colon V(G)\rightarrow \{0,1,2,\ldots\}$ such that $|f(u)-f(v)|\geq {\rm diam}(G)+1-d(u,v)$ for each pair of distinct vertices $u,v\in V(G)$, where $\rm ...
Saha, Laxman, Basunia, Alamgir Rahaman
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